Approximation of multipliers-Reference-Cited by-同舟云学术

Approximation of multipliers

Published:1974 Issue:2 Volume:44 Page:381-384
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Gaudry Garth I.,Inglis Ian R.

Abstract

We note some necessary and sufficient conditions concerning norm approximation of Fourier multipliers, and give an example to show that M q ( Z ) {M_q}(Z) , the space of Fourier multipliers of type ( q , q ) (q,q) , is not norm dense in M p ( Z ) {M_p}(Z) when 1 ≦ q > p ≦ 2 1 \leqq q > p \leqq 2 . An extension of this example to more general groups is indicated.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1974-044-02/S0002-9939-1974-0340970-8/S0002-9939-1974-0340970-8.pdf

Reference6 articles.

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2. Uniform approximation on noncompact spaces;Edwards, R. E.;Trans. Amer. Math. Soc.,1966

3. Translation invariant operators in 𝐿^{𝑝};Figà-Talamanca, Alessandro;Duke Math. J.,1965

4. Multipliers of 𝐿^{𝑝} which vanish at infinity;Figà-Talamanca, Alessandro;J. Functional Analysis,1971

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